English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We give the first numerical calculation of the spectrum of the Laplacianacting on bundle-valued forms on a Calabi-Yau three-fold. Specifically, we showhow to compute the approximate eigenvalues and eigenmodes of the DolbeaultLaplacian acting on bundle-valued $(p,q)$-forms on K\"ahler manifolds. Werestrict our attention to line bundles over complex projective space andCalabi-Yau hypersurfaces therein. We give three examples. For two of these,$\mathbb{P}^3$ and a Calabi-Yau one-fold (a torus), we compare our numericswith exact results available in the literature and find complete agreement. Forthe third example, the Fermat quintic three-fold, there are no known analyticresults, so our numerical calculations are the first of their kind. Theresulting spectra pass a number of non-trivial checks that arise from Serreduality and the Hodge decomposition. The outputs of our algorithm include allthe ingredients one needs to compute physical Yukawa couplings in stringcompactifications.

Numerical spectra of the Laplacian for line bundles on Calabi-Yau hypersurfaces